Soak the mushrooms. Place the dried shiitake in a container with 2 cups of room-temperature water. Cover and refrigerate overnight until fully rehydrated. Trim off any tough stems and leave the small caps whole. Strain the soaking liquid and reserve 1 cup for braising.
Season the chicken. Place the chicken in a large bowl. Add the salt and ½ tablespoon wine, then mix well. Add the starch and toss to coat.
Prep the aromatics. Thinly slice the ginger on a diagonal. Cut the scallions into 2-inch sections, keeping the white and green parts separate.
Sear the chicken. Add 1 tablespoon avocado oil to a 4-quart Dutch oven and preheat over medium-low heat until hot. Arrange the chicken in a single layer. Increase the heat to medium or medium-high to maintain a steady sizzle. Sear until golden brown, about 4 minutes on the first side and 2–3 minutes on the second side. The chicken does not need to be cooked through yet.
Sauté the aromatics. Turn off the heat and transfer the chicken to a plate, leaving the oil and rendered fat in the pot. Add up to 1 more tablespoon of oil if needed. Return the heat to medium. Add the ginger and scallion whites and sauté for about 1 minute, until fragrant.
Braise the chicken. Return the chicken to the pot and stir briefly. Add the shiitake, light soy sauce, dark soy sauce, remaining 3 1⁄2 tablespoons of wine, brown sugar, and 1 cup strained mushroom soaking liquid. Stir well and bring to a simmer over medium heat. Cover and simmer for 8–10 minutes, opening the lid periodically to stir along the bottom of the pot. Adjust the heat between medium and medium-low to keep the sauce bubbling steadily without scorching. The sauce should become glossy and begin to thicken, with plenty left in the pot.
Add the chestnuts. Gently stir in the cooked chestnuts. Cover and simmer over medium-low heat for 5 minutes, stirring periodically to prevent sticking.
Finish and serve. Add the scallion greens and stir for 30 seconds. Turn off the heat. The sauce will thicken further as it cools, so leave enough to spoon over the chicken and rice. Transfer to a serving bowl and serve hot with rice.
Notes
Dried shiitake: These give the sauce a deep, woodsy flavor. Stick to the listed amount—in my testing, adding more made the sauce taste too salty and the mushroom flavor overpowering.
Fresh shiitake option: Use 5 oz fresh shiitake, about 5 large caps. Trim off the tough stems and slice the caps. Skip the soaking step and use 1 cup chicken broth in place of the mushroom soaking liquid. The flavor will be less woodsy.
Frozen chestnuts: Use peeled, raw frozen chestnuts straight from the freezer. Add them in Step 6 with the chicken, mushrooms, and braising liquid. Cover and simmer for 15–20 minutes total, stirring periodically, until the chestnuts are soft and buttery. Skip Step 7 and finish with the scallion greens.
Clay pot method: I sear the chicken in a separate skillet before transferring it to my clay pot. For the simplest method, use a Dutch oven so you can sear, sauté, and braise in the same pot.
Storage and reheating: Store leftovers in an airtight container in the refrigerator for up to 4 days. Reheat on the stovetop with a splash of chicken stock to loosen the sauce, stirring until warmed through.